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Algebric Expression

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Joined: 18 Jun 2009
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Concentration: Strategy, General Management
Schools: Stanford '14 (D), Booth '14 (D), Johnson '14 (D)
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Algebric Expression [#permalink] New post 09 Apr 2010, 13:58
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Question Stats:

0% (00:00) correct 100% (00:56) wrong based on 0 sessions
If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)?
(a) 9.
(b) 12.
(c) 15.
(d) 16.
(e) 18.

Kindly support your answer with explanation.
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Re: Algebric Expression [#permalink] New post 09 Apr 2010, 17:06
First step is to expand the expression (2X + Y)(2Z + W) via FOIL:
2X*2Z + 2X*W + Y*2Z + Y*W
4XZ + 2XW + 2YZ + YW
Rearranging the terms we get:
(4XZ + YW) + 2(XW + YZ)
(4XZ + YW) + 2(XW + YZ)

All we need to do now is substitute the values 4XZ + YW = 3 and XW + YZ = 6
(4XZ + YW) + 2(XW + YZ)
3 + 2*6
= 15

Answer C
Re: Algebric Expression   [#permalink] 09 Apr 2010, 17:06
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